Least Common Multiple (LCM) of 105 and 171
The least common multiple (LCM) of 105 and 171 is 5985.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 105 and 171?
First, calculate the GCD of 105 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 171 = 0 remainder 105 |
| 2 | 171 ÷ 105 = 1 remainder 66 |
| 3 | 105 ÷ 66 = 1 remainder 39 |
| 4 | 66 ÷ 39 = 1 remainder 27 |
| 5 | 39 ÷ 27 = 1 remainder 12 |
| 6 | 27 ÷ 12 = 2 remainder 3 |
| 7 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 63 | 6363 |
| 122 and 67 | 8174 |
| 114 and 185 | 21090 |
| 172 and 179 | 30788 |
| 118 and 23 | 2714 |